It is possible that the DNS for your domain has not fully propagated, the move means your domain is pointed to a different IP.
Could also be that cPanel and your site is served by different services on the server. Site being handled by Apache, while cPanel (and cPanels backend) has its own way of handling requests independently from Apache (don't quote me on this though, but it is not uncommon for one to work and not the other when servers are stressed).